Question: A set of four consecutive integers has a sum of 22. If each integer of the set is increased by 2 and then multiplied by 20, what is the sum of the new set of integers?
Solution: Increasing each integer by 2 will increase their sum by $2\cdot 4 = 8$, meaning the sum after this step is $22 + 8 = 30$. Multiplying each integer by 20 will multiply the entire sum by 20, leading to a final sum of $30\cdot 20 = \boxed{600}$.